Marek-Jerzy Pindera
Applied Mechanics Program, University of Virginia, USA

Thermo-Mechanical Analysis of Functionally Graded Thermal Barrier Coatings with Actual and Homogenized Microstructures

The majority of techniques employed for the analysis of functionally graded materials (FGMs) use the so-called uncoupled approach which is based on homogenized material property variations and thus ignores the effect of microstructural gradation. The higher-order theory for functionally graded materials (HOTFGM) [1] is a coupled approach which explicitly takes the effect of microstructural gradation, and thus the local-global interaction of the spatially variable inclusion phase(s), into account. Despite its demonstrated utility, however, the original formulation of HOTFGM is computationally intensive. Therefore, an efficient reformulation of HOTFGM has been developed based on the local-global conductivity and stiffness matrix formulation [2]. In this approach, surface-averaged quantities are the primary variables that replace volume-averaged quantities employed in the original formulation. The reformulation decreases the size of the global conductivity and stiffness matrices by approximately sixty percent, facilitating modeling of realistic microstructures [3].
To demonstrate the utility of the reformulated higher-order theory, a technologically important example of a thermal barrier coating with graded microstructure is presented. The analysis is performed taking the coating's actual microstructure into account, and then repeated using layerwise homogenized properties. These properties are calculated using a new micromechanics model that combines elements of the homogenization theory with the higher-order theory within a unified framework [4]. Herein, this new micromechanics model is also reformulated for increased efficiency. The effect of the graded coating's microstructure on the local stress and displacement fields is demonstrated and compared with the corresponding results obtained using the layerwise homogenized properties. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing FGMs.

References
[1] Aboudi, J., Pindera, M-J. and Arnold, S. M., Higher-Order Theory for Functionally Graded Materials, Composites Part B: Engineering, Vol. 30, No. 8 (1999), pp. 777-832.
[2] Pindera, M-J., Local/Global Stiffness Matrix Formulation for Composite Materials and Structures, Composites Engineering, Vol. 1, No. 2 (1991), pp. 69-83.
[3] Bansal, Y. and Pindera, M-J., Efficient Reformulation of the Thermoelastic Higher-Order Theory for FGMs, NASA CR 211909, NASA-Glenn Research Center, Cleveland, OH, 2002.
[4] Aboudi, J., Pindera, M-J., and Arnold, S.M., Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials, J. Applied Mechanics, Vol. 68, No. 5, 2001, pp. 697-707.